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  2. Involute gear - Wikipedia

    en.wikipedia.org/wiki/Involute_gear

    The involute gear profile, sometimes credited to Leonhard Euler, [1] was a fundamental advance in machine design, since unlike with other gear systems, the tooth profile of an involute gear depends only on the number of teeth on the gear, pressure angle, and pitch. That is, a gear's profile does not depend on the gear it mates with.

  3. List of gear nomenclature - Wikipedia

    en.wikipedia.org/wiki/List_of_gear_nomenclature

    Form diameter is the diameter of a circle at which the trochoid (fillet curve) produced by the tooling intersects, or joins, the involute or specified profile. Although these terms are not preferred, it is also known as the true involute form diameter (TIF), start of involute diameter (SOI), or when undercut exists, as the undercut diameter.

  4. Involute - Wikipedia

    en.wikipedia.org/wiki/Involute

    In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut string as the string is either unwrapped from or wrapped around the curve. [1] The evolute of an involute is the original curve.

  5. Gear - Wikipedia

    en.wikipedia.org/wiki/Gear

    The surface of action for involute, parallel axis gears with either spur or helical teeth. It is tangent to the base cylinders. Zone of action (contact zone) For involute, parallel-axis gears with either spur or helical teeth, is the rectangular area in the plane of action bounded by the length of action and the effective face width. Path of ...

  6. Cycloid gear - Wikipedia

    en.wikipedia.org/wiki/Cycloid_gear

    Involute designs for these leaves would be undercut, making them too fragile and difficult to manufacture. 3. A large aspect of the design of watch and clock movements is the minimisation of friction. Involute gear teeth often mesh with 2 to 3 points of contact at once. Cycloidal gears can be made so there are only 1 to 2 points of contact.

  7. Radius of curvature - Wikipedia

    en.wikipedia.org/wiki/Radius_of_curvature

    Let γ be as above, and fix t.We want to find the radius ρ of a parametrized circle which matches γ in its zeroth, first, and second derivatives at t.Clearly the radius will not depend on the position γ(t), only on the velocity γ′(t) and acceleration γ″(t).

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    You can find instant answers on our AOL Mail help page. Should you need additional assistance we have experts available around the clock at 800-730-2563.

  9. Goat grazing problem - Wikipedia

    en.wikipedia.org/wiki/Goat_grazing_problem

    Find the area between a circle and its involute over an angle of 2 π to −2 π excluding any overlap. In Cartesian coordinates, the equation of the involute is transcendental; doing a line integral there is hardly feasible. A more felicitous approach is to use polar coordinates (z,θ).